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Acta Informatica

, Volume 17, Issue 2, pp 157–184 | Cite as

A new data structure for representing sorted lists

  • Scott Huddleston
  • Kurt Mehlhorn
Article

Summary

In this paper we explore the use of weak B-trees to represent sorted lists. In weak B-trees each node has at least a and at most b sons where 2ab. We analyse the worst case cost of sequences of insertions and deletions in weak B-trees. This leads to a new data structure (level-linked weak B-trees) for representing sorted lists when the access pattern exhibits a (time-varying) locality of reference. Our structure is substantially simpler than the one proposed in [7], yet it has many of its properties. Our structure is as simple as the one proposed in [5], but our structure can treat arbitrary sequences of insertions and deletions whilst theirs can only treat non-interacting insertions and deletions. We also show that weak B-trees support concurrent operations in an efficient way.

Keywords

Information System Operating System Data Structure Communication Network Information Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Bayer, R.: Symmetric Binary B-trees: Data structures and maintenance algorithms. Acta Informat. 1, 290–306 (1972)Google Scholar
  2. 2.
    Bayer, R., McCreight, E.: Organization and maintenance of large ordered indizes. Acta Informat. 1, 173–189 (1972)Google Scholar
  3. 3.
    Bayer, R., Schkolnik, M.: Concurrency of operations on B-trees. Acta Informat. 9, 1–21 (1977)Google Scholar
  4. 4.
    Blum, N., Mehlhorn, K.: On the average number of rebalancing steps in weight-balanced trees. Theor. Comput. Sci. 11, 303–320 (1980)Google Scholar
  5. 5.
    Brown, M.R., Tarjan, R.E.: Design and analysis of a data structure for representing sorted lists. SIAM J. Comput. 9, 594–614 (1980)Google Scholar
  6. 6.
    Guibas, L.J., Sedgewick, R.: A dichromatic framework for balanced trees. Proc. 19th Annual Symposium on Foundations of Computer Science. Ann Arbor: IEEE Computer Socienty, pp. 8–21 (1978)Google Scholar
  7. 7.
    Guibas, L., McCreight, E., Plass, M, Roberts, J.: A new representation for linear lists. 9th ACM Symposium on Theory of Computing Boulder, pp. 49–60 (1977)Google Scholar
  8. 8.
    Huddleston, S.: Robust balancing in B-trees. PhD Dissertation, Computer Science Department, University of Washington, Seattle, 1981Google Scholar
  9. 9.
    Huddleston, S., Mehlhorn, K.: Robust balancing in B-trees. 5th GI-Conference on Theoretical Informatics 1981, Karlsruhe, LNCS 104, 234–244 (1981)Google Scholar
  10. 10.
    Maier, D., Salveter, S.C.: Hysterical B-trees. Technical Report 79/007, Dept. of Computer Science, State University of New York at Stony Brook, November 1979Google Scholar
  11. 11.
    Mehlhorn, K.: Effiziente Algorithmen. Teubner-Verlag, Studienbücher Informatik 1977Google Scholar
  12. 12.
    Mehlhorn, K.: Sorting presorted files. 4th GI-Conference on Theoretical Computer Science 1979, Aachen, Lecture Notes in Computer Science Vol. 67, pp. 199–212. Berlin-Heidelberg-New York: Springer 1979Google Scholar
  13. 13.
    Mehlhorn, K.: Searching, sorting and information theory. MFCS 79, Lecture Notes in Computer Science Vol. 74, pp. 131–145. Berlin-Heidelberg-New York: Springer 1981Google Scholar
  14. 14.
    Willard, D.E.: The super-B-tree algorithm. Harvard Aiken Computation Laboratory Report TR-03-79Google Scholar

Copyright information

© Springer-Verlag 1982

Authors and Affiliations

  • Scott Huddleston
    • 1
  • Kurt Mehlhorn
    • 2
  1. 1.Scott Huddleston, Information and Computer ScienceUniversity of California, IrvineIrvineUSA
  2. 2.Kurt Mehlhorn, FB 10 - InformatikUniversität des SaarlandesSaarbrückenWest Germany

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